What are the achievements of Logic?

What is the basis for reason? And mathematics?

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Dapplegrim
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What are the achievements of Logic?

Post by Dapplegrim » Mon Nov 27, 2017 12:31 pm

What are the achievements of logic? It would seem to be hard to identify them.

In contrast mathematics has huge achievements to its name, especially its use in the domain of physics.

But logic, whether pure and abstract or its application to language, does not have many, if any, achievements to its name.

'Socrates is mortal' and 'It is raining' - two classical conclusions of logic, can hardly be claimed as achievements.

Its main claim would seem to be that it claims to be 'true'. But by what logic is that claim to truth justified? And also what is meant by 'true' when applied to logic? It would appear to be only a label to indicate internal self-consistency.

Does philosophy need this form of logic? If so what for?

Does anyone have any suggestions?

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Eodnhoj7
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Re: What are the achievements of Logic?

Post by Eodnhoj7 » Mon Nov 27, 2017 1:15 pm

Structure and definition corresponding to truth values and their corresponding grades, considering what we understand of truth is merely definition through structure.

alan1000
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Re: What are the achievements of Logic?

Post by alan1000 » Sat Jan 27, 2018 4:30 pm

You haven't heard that all of mathematics is reducible to logic? I'm not in a position to argue the case, but I understood that this had been achieved by about the beginning of the 20th C, due to the efforts of Russell, Frege, Whitehead et al.

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Necromancer
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Re: What are the achievements of Logic?

Post by Necromancer » Sat Jan 27, 2018 6:00 pm

alan1000 wrote:
Sat Jan 27, 2018 4:30 pm
You haven't heard that all of mathematics is reducible to logic? I'm not in a position to argue the case, but I understood that this had been achieved by about the beginning of the 20th C, due to the efforts of Russell, Frege, Whitehead et al.
Math is math and logic is logic for very good reasons. They really do not go together. Numbers for math and relations of language for logic. :?: :D

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-1-
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Re: What are the achievements of Logic?

Post by -1- » Sat Jan 27, 2018 7:32 pm

Necromancer wrote:
Sat Jan 27, 2018 6:00 pm
alan1000 wrote:
Sat Jan 27, 2018 4:30 pm
You haven't heard that all of mathematics is reducible to logic? I'm not in a position to argue the case, but I understood that this had been achieved by about the beginning of the 20th C, due to the efforts of Russell, Frege, Whitehead et al.
Math is math and logic is logic for very good reasons. They really do not go together. Numbers for math and relations of language for logic. :?: :D
Actually, Necromancer, Alan1000 is right. All math reduced to logic and shown that it's nothing but, has been written in a book called "Principia Mathematika", by some smart dude. He said after finishing the tome, that he got forever exhausted... he felt lethargic for the rest of his natural life, he got so much of his brain and mental work put into it.

And then some schmucks come around and declare that they don't know it, so it does not exist.

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Eodnhoj7
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Re: What are the achievements of Logic?

Post by Eodnhoj7 » Sat Jan 27, 2018 9:39 pm

alan1000 wrote:
Sat Jan 27, 2018 4:30 pm
You haven't heard that all of mathematics is reducible to logic? I'm not in a position to argue the case, but I understood that this had been achieved by about the beginning of the 20th C, due to the efforts of Russell, Frege, Whitehead et al.
Algebra specifically if I remember correctly, but your point rings true in some facet of memory.

Impenitent
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Re: What are the achievements of Logic?

Post by Impenitent » Sun Jan 28, 2018 12:43 am

I'm sure it won a participation trophy once...

-Imp

Londoner
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Re: What are the achievements of Logic?

Post by Londoner » Sun Jan 28, 2018 5:30 pm

alan1000 wrote:
Sat Jan 27, 2018 4:30 pm
You haven't heard that all of mathematics is reducible to logic? I'm not in a position to argue the case, but I understood that this had been achieved by about the beginning of the 20th C, due to the efforts of Russell, Frege, Whitehead et al.
On the contrary, they failed to do this. There were always paradoxes that could not be incorporated. Later, Gödel's incompleteness theorems showed why this would always be the case.

wtf
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Re: What are the achievements of Logic?

Post by wtf » Sun Jan 28, 2018 9:00 pm

alan1000 wrote:
Sat Jan 27, 2018 4:30 pm
You haven't heard that all of mathematics is reducible to logic? I'm not in a position to argue the case, but I understood that this had been achieved by about the beginning of the 20th C, due to the efforts of Russell, Frege, Whitehead et al.
I'm curious as to where you're getting your information. Of course this statement is wrong as already noted. Gödel's incompleteness theorems show that mathematical truth can not be reduced to logic.

But I saw your post on infinity over on that other site and virtually everything you say is laughably incorrect. You're just getting bad information and misunderstanding even that.

Where are you getting your math from? Just wondering.

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Greta
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Re: What are the achievements of Logic?

Post by Greta » Sun Jan 28, 2018 11:30 pm

Dapplegrim wrote:
Mon Nov 27, 2017 12:31 pm
What are the achievements of logic? It would seem to be hard to identify them.

In contrast mathematics has huge achievements to its name, especially its use in the domain of physics.

But logic, whether pure and abstract or its application to language, does not have many, if any, achievements to its name.

'Socrates is mortal' and 'It is raining' - two classical conclusions of logic, can hardly be claimed as achievements.

Its main claim would seem to be that it claims to be 'true'. But by what logic is that claim to truth justified? And also what is meant by 'true' when applied to logic? It would appear to be only a label to indicate internal self-consistency.

Does philosophy need this form of logic? If so what for?

Does anyone have any suggestions?
Incompleteness does look like the last word in this; if you can't calculate everything then all calculations are necessarily relative to initial assumptions rather than an absolute. Interestingly, if one attempted to construct a supercomputer capable of calculating everything, it's believed that the computer would become so large that the pressure in the centre would form a planetary core - perhaps not ideal for computing (never mind heat frying components long before that).

wtf
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Re: What are the achievements of Logic?

Post by wtf » Mon Jan 29, 2018 3:47 am

Greta wrote:
Sun Jan 28, 2018 11:30 pm
Interestingly, if one attempted to construct a supercomputer capable of calculating everything, it's believed that the computer would become so large that the pressure in the centre would form a planetary core - perhaps not ideal for computing (never mind heat frying components long before that).
Who believes nonsense like that? You're not known for posting silliness. Where did this come from?

Turing proved in 1936 that there are easily stated problems that no computation can solve. This result is essentially the same as Gödelian incompleteness.

Pressure in the center would form a planetary core? WTF? That's really out of left field, extremely bizarre remark. I only say this because it's unexpected from you.

https://en.wikipedia.org/wiki/Halting_problem

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Greta
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Re: What are the achievements of Logic?

Post by Greta » Mon Jan 29, 2018 5:16 am

wtf wrote:
Mon Jan 29, 2018 3:47 am
Greta wrote:
Sun Jan 28, 2018 11:30 pm
Interestingly, if one attempted to construct a supercomputer capable of calculating everything, it's believed that the computer would become so large that the pressure in the centre would form a planetary core - perhaps not ideal for computing (never mind heat frying components long before that).
Who believes nonsense like that? You're not known for posting silliness. Where did this come from?

Turing proved in 1936 that there are easily stated problems that no computation can solve. This result is essentially the same as Gödelian incompleteness.

Pressure in the center would form a planetary core? WTF? That's really out of left field, extremely bizarre remark. I only say this because it's unexpected from you.

https://en.wikipedia.org/wiki/Halting_problem
It was a curio for entertainment's sake. I was just agreeing with you otherwise.

I can't find it now but the idea came from a mathematician interviewed on Through the Wormhole who had done calculations that left him with the postulation that it's impossible to know everything because, if a computer that was supposed to calculate everything was created, as it grew it would eventually collapse under its own weight to form a black hole. I just extrapolated that heat etc would stymie the machine long before collapse into a black hole.

wtf
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Re: What are the achievements of Logic?

Post by wtf » Mon Jan 29, 2018 5:27 am

Greta wrote:
Mon Jan 29, 2018 5:16 am
It was a curio for entertainment's sake. I was just agreeing with you otherwise.
Didn't mean to seem to attack out of left field. You're one of the sane ones here which is why your remark struck me as off.
Greta wrote:
Mon Jan 29, 2018 5:16 am
I can't find it now but the idea came from a mathematician interviewed on Through the Wormhole who had done calculations that left him with the postulation that it's impossible to know everything because, if a computer that was supposed to calculate everything was created, as it grew it would eventually collapse under its own weight to form a black hole.
Oh my. He was misinformed or not being serious. We already know of problems computers can't solve. Turing showed that. Building a larger computer wouldn't help in the least. This is well known but evidently not to this person on tv. Perhaps he was trying to make a point in a popularized way.

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Greta
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Re: What are the achievements of Logic?

Post by Greta » Mon Jan 29, 2018 11:59 am

wtf wrote:
Mon Jan 29, 2018 5:27 am
Greta wrote:
Mon Jan 29, 2018 5:16 am
It was a curio for entertainment's sake. I was just agreeing with you otherwise.
Didn't mean to seem to attack out of left field. You're one of the sane ones here which is why your remark struck me as off.
Greta wrote:
Mon Jan 29, 2018 5:16 am
I can't find it now but the idea came from a mathematician interviewed on Through the Wormhole who had done calculations that left him with the postulation that it's impossible to know everything because, if a computer that was supposed to calculate everything was created, as it grew it would eventually collapse under its own weight to form a black hole.
Oh my. He was misinformed or not being serious. We already know of problems computers can't solve. Turing showed that. Building a larger computer wouldn't help in the least. This is well known but evidently not to this person on tv. Perhaps he was trying to make a point in a popularized way.
The theme of the show was generally about the problems with knowing everything. A variety of thinkers were interviewed, each taking a different angle. They'd already been through Gödel's incompleteness theorems and other less colourful perspectives, and I think the idea was basically that, even if all other factors were not present, it is not even physically possible to calculate everything. Basically, it was the final kicker for any doubters who may have found other approaches too heady or confusing to be convincing.

Thanks for saying I'm sane - I probably just seem so by philosophy forum standards :D

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Arising_uk
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Re: What are the achievements of Logic?

Post by Arising_uk » Mon Jan 29, 2018 3:21 pm

Dapplegrim wrote:What are the achievements of logic? It would seem to be hard to identify them. ...
The computer you type upon is designed upon it.
Does philosophy need this form of logic? If so what for?

Does anyone have any suggestions?
Reasoning.

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